Note that if \(u\)  is compactly supported, then we would be able to find \(t^\ast \)  such that \(u(t^\ast ,x)=0\) , where \(x\)  varies on some open set of \(\mathbb {E}\) . As we shall see, the demonstration of Theorem 2.2 implies that if this happens, then \(u\)  necessarily vanishes everywhere. This is a fact also known for the CH equation, see [1]}, [2]}.
